Hello!

Any help with the following is really appreciated (hints, as well!):

For $\displaystyle f \in L^{1} ( \mathbb{R} ) $ and $\displaystyle s \in \mathbb{R} $, let

$\displaystyle \hat{f} (s) = \int_{\mathbb{R}} f (t) e^{-ist} dt

$

Prove that $\displaystyle \hat{f} (s) \rightarrow 0

$ as $\displaystyle |s| \rightarrow \infty

$

We're allowed to use the 'strong operator convergence' theorem for Banach spaces, as well as other standard results in Banach spaces.